Introduction

This chapter deals with the special case of
HeNe lasers that have their frequency actively
regulated either directly, or indirectly via control of intensity. Their
output is generally either a single longitudinal mode (single optical
frequency), a pair of adjacent longitudinal modes (two optical frequencies
separated by 600 MHz to 1 GHz typical), or a pair of optical frequencies close
together produced by Zeeman splitting of a single longitudinal mode
(250 kHz to 8 Mhz typical) or an Acousto-Optic Modulator (AOM) generating
a sideband of a single longitudinal mode (20 MHz typical).

In almost all cases, these apply specifically to HeNe lasers operating
on the so-called red transition around 633 nm (although when stabilized,
there may be many many places to the right of the decimal point). HeNe
lasers on other wavelengths can also be stabilized, though not all the
same techniques can be used. This chapter deals almost exclusively
with stabilized red HeNe lasers.

General information on HeNe lasers as well as a brief introduction to
stabilized HeNe lasers and typical locking schemes
may be found in the chapter: Helium-Neon
Lasers. Here, we delve into the topic in more detail.

However, it is not intended to be an all encompassing treatise on stabilized
laser with all the gory details including hairy math. :) For that, refer to
the scientific literature, most from the 1960s or 1970s. Only
a few references are included here, but Web searches will turn up numerous
research papers, many of which are in the public domain. For those that
are not, affiliation with a major university or other academic institution
may be required to access them for free.

The popular conception of a laser is that it is a light source of a single
specific color or wavelength. While such a description is good enough for
most Mark I eyeballs (at least where the wavelength is in the visible
spectrum), the output from real lasers is usually not so perfect.

The behavior of any laser is determined by many factors but the most important
two are:

Lasing gain medium: When "pumped" by a suitable excitation source,
it provides amplification by stimulated emission for photons over a specific
range of wavelengths.

For the red HeNe laser, the gain medium is a mixture of helium and neon gases
at low pressure excited by an electrical discharge. The helium helps with
the excitation while the neon actually provides the gain. The 633 nm red
wavelength is only one of several that HeNe lasers can use, but nearly
all HeNe lasers that are actively stabilized are red. :)

Laser cavity or resonator: A structure usually consisting of
mirrors to provide optical feedback at the desired laser wavelength.

For most stabilized HeNe lasers, a Fabry-Perot configuration is
used with the gain medium between a pair of precisely aligned mirrors.
These are all part of the sealed HeNe laser tube.

The useful output of most stabilized HeNe lasers is either a (ideally) single
optical frequency, or a pair of optical frequencies separated by anywhere
from a few 10s of kHz to hundreds of MHz.
And in some applications, multiple frequencies (usaully 2 but it could be
more) that are locked to a reference may be useful.

The purpose of locking in a stabilized HeNe laser is to assure that the
desired output (single or two frequencies in most cases) has a controlled.
optical frequency or frequencies. For use
in metrology applications, this will mean that the single or
dual lasing line is fixed at a known optical frequency (corresponding
to a known wavelength related by c/f where c is the speed of light and f is
the optical frequency). Therefore, the locking controller needs
a reference, which can be intrinsic or extrinsic. An intrinsic
reference uses the properties of the laser itself. An extrinsic reference
requires some external device such as another laser (which itself has
been locked to a known optical frequency), a gas cell having known spectral
absorption with respect to optical frequency, or a physical device like
a super high finesse Fabry-Perot etalon or interferometer. The chart below
summaries the most popular locking techniques for red (~633 nm) HeNe lasers:

The useful output of these are NOT always absolutely pure single mode or
single optical frequency limited by the laser dynamics:

* denote techniques where the output has either a pair of modes of
similar amplitude close together in optical frequency, or a small "ghost
mode" next to the main mode.

+ denotes techniques based on Pound-Drever-Hall locking or a similar
implementation that adds some dither to the optical frequency.

The approaches listed in the first group are intrinsic and use the Neon Gain
Curve (NGC) of the HeNe laser tube as the reference. The center of the NGC
has an optical frequency which depends only on the neon isotope
ratio, temperature, and pressure, all of which can be controlled
fairly precisely. The gain bandwidth of the NGC is also relatively
narrow (as these things go) at around 1.6 GHz which can both limit
the number of longitudinal modes that are oscillating (more on this
below) and make feedback using its profile be more precise.
Thus the NGC can be used to accurately position
the lasing line(s) at a known location. All but the most exotic (and
expensive!) stabilized HeNe lasers use one of the intrinsic techniques
based on the NGC listed above. The vast majority use single or two
mode polarization stabilization.

Relatively simple approaches using an external F-P resonator or other
type of interferometer are possible. For example, using a low finesse
Scanning Fabry-Perot Interferometer (SFPI) to monitor the longitudinal
modes with a digital control loop maintaining them in a specific location
on the NGC can be used with three mode polarization stabilization to
obtain higher power with one mode centered. Single and dual mode
polarization stabilization are limited to a maximum of around 2 mW;
three mode stabilization is capable of up to around 3.5 mW or a bit more.
But this is still an intrinsic technique. (This could also be used
for single or dual mode stabilization but would probably not provide
much, if any, benefit.)

It should be noted that it is because the gain bandwidth of neon is
relatively narrow at 1.6 GHz, that the NGC becomes so useful. Solid state
(SS) lasers on the other hand have lasing medium gain bandwidths typically
wider by a factor of 50 or more. While straightforward techniques can
be used to force single mode in an SS laser, achieving precise
control of optical frequency with such a wide gain bandwidth is more difficult.
This is one of the primary reasons that SS lasers have for the most part as
yet been unable to replace the lowly HeNe laser in applications requiring
optical frequency accuracy and stability. Locking diode lasers at a
specific optical frequency is even more complex.

Of the extrinsic technigues,
a stabilized HeNe laser making use of an iodine cell is probably the most
precise optical frequency reference available commercially (with an equally
high price to match). Its absolute optical frequency accuracy may be
two orders of magnitude better than the technique of
two-mode polarization stabilization, used in most commercial stabilized
HeNe lasers now and in the past.

Going beyond this level of precision to high finesse F-P resonators and such is
generally the perview of advanced research. To get down to that
<1 Hz requires massive isolation chambers and active damping to minimize
vibration and other external influences. Such a system is not likely to be
portable! ;-)

The chart excludes any technques requiring use of intra-cavity devices like
etalons to force single frequency operation. These are capable of both
high power AND high stability but require special tubes and relatively
complex control. Thus they are expensive and not at all common, though
at least one company does claim to offer a 40 mW single frequency HeNe
laser.

Having said all that, it's remarkably simple - almost trivial - to control
the behavior of a common HeNe laser tube similar to those that used to be
found in grocery store barcode scanners to provide a single frequency
output with a stability of better than 1 part in 10,000,000. In fact,
it can be done with a total of 4 parts costing only a couple dollars (besides
the laser tube and power supplies). Nearly every possible technique imaginable
has been explored at some time in the past. It's quite possible that trained
pigeons have even been pressed into service for this purpose, and there's
probably a patent on it. ;-) What are described here are only the most
common (electronic) approaches.

But before any of these can be described in more detail, a primer or
laser modes is required.

For everything that follows, it is assumed that the spatial mode structure
of the HeNe laser is near pure TEM00 resulting in close to a Gaussian beam
profile. We are not aware of any stabilized HeNes using multi-spatial
mode tubes.

Lasing is determined by the round trip gain at the laser's optical frequency
or wavelength, and resonance wihin the laser cavity. For everything in
this chapter, we assume a linear "Fabry-Perot" cavity - the
classic "gain medium between mirrors" laser - and the one used in virtually
all HeNe lasers and even close to all stabilized HeNe lasers. But ring and
other geometries would have similar constraints.

As with any resonant structure, there will be a fundamental frequency at
which it can respond (n=1), as well as an inifinite range of harmonics
(n=2,3,4.....infinity). For an organ pipe or violin string resosnance is
at its fundamental and several harmonics. However, due to the short
wavelength of light and relatively large resonant cavity length, for
a HeNe laser, there is no fundamental and the harmonics have values of
n in the hundreds of thousands or more.

In order to sustain laser oscillation, the round trip gain must exceed losses
for photon at an optical frequency that is close to a cavity resonance
as defined by n*c/2L. L is the distance between the mirrors, c is the
speed of light, and n is an integer that results in the equation being
equal to an optical frequency with a net gain greater than
one for the lasing medium gain and cavity geometry.

For a red (633 nm) HeNe laser, the Neon Gain Curve (NGC) has a width of
1.5 to 1.6 GHz FWHM and is centered at around 474 THz. (We will have much
more precise values later.) As an example, for a cavity length
of 200 mm, c/2L is around 725 MHz. Thus, 1 to 3 modes may oscillate
at the same time depending on their precise position within the NGC,
but never more than that. Typical values for n in this case
would be successive integers near 987,500.
(There are other more subtle effects such as mode pulling and
mode pushing that offset the actual optical frquencies by a small amount,
but for now, the exact cavity resonances are sufficiently accurate.)

Higher power longer tubes will support more than 3 modes. And due to the
shape of the NGC, the power in the strongest mode increases sub-linearly
with tube length. So even if it could be isolated for a single frequency
laser (which beyond 3 is not really practical), its power would not be
that high, perhaps 6 mW for a tube outputting 35 mW . Further,
due to mode competition, the power in each mode in longer tubes tends to
fluctuate at random among them and stabilization doesn't help. This can
be an issue even with the tube used in three mode stabilization.

When a HeNe laser is powered, whichever cavity resonances - also called
"cavity modes" are within the NGC and have sufficient round trip gain
will lase. These are the longitudunal or axial
modes of the laser. Each of these "lasing lines" is a very nearly pure
optical frequency in a HeNe laser, with a bandwidth of under 1 kHz and
possibly as low as a few Hz or less. Thus, the term "single frequency"
is appropriate (except for the most die-hard purists) where one of these
modes is the output of a stabilized laser.

If the distance between the mirrors changes, the position of the modes
will drift through the NGC. For large frame laboratory HeNe lasers,
the resonator structure is designed to have a very low coefficient of
thermal expansion. However, for common HeNe laser tubes of the
type used in most stabilized HeNe lasers, the heating effects of the
plasma discharge will cause the distance between the mirrors the change.
As this occurs, the longitudinal modes will drift through the NGC. A
mode at the high frequency-end will eventually disappear and be replaced by a
new one appearing at the low-frequency-end. This is "mode sweep". An
animation of the mode behavior of a tube similar to those used in many
stabilized HeNes can be found at HeNe Laser Mode
Sweep: 200 mm (~8 inch) Cavity Length. Of course, the movement is
continuous but it's tiring to create an infinite number of slides. ;-)

To stabilize such a tube, the cavity length needs to be controlled in a
feedback loop. A variety of means can be used to affect cavity length.
A heater wrapped around the tube is most common, but others include
an internal heater wrapped around the bore, an induction heater on
one of the mirror mount stems, or the use of a PeiZo Transducer (PZT)
behind one of mirror. It's even possible to use a magnetic actuator to
press on one of the mirror mounts. With stabilization, the longitudinal
modes can be precisely "parked" on the NGC. It's possible to do this in
the animation by careful use of the left and right arrow keys to keep
one mode centered. Fortunately, analog or digital electronics is much
more effective and doesn't get tired as easily. ;-)

All intrinsic HeNe stabilization techniques are based on
controlling the mode position using the NGC itself as the optical
frequency reference. Thus, depending on what precision is required,
its absolute optical frequency, width, and profile must be known.
These are affected primarily by the temperature, pressure, and
He:Ne isotope ratio in the tube. However, due to mode competition,
the length of the tube may have a significant effect on the shape
of the NGC, especially for the shorter tubes of interest here.

Note that while the NGC is discussed, it is actually the "Laser Output
Power Curve" or LOPC that provides the input variables for most of these
techniques. However, we may use the two interchangeably in discussions,
even though purists will probably object. :)

All stabilization schemes are based on the precise control of the HeNe laser's
cavity length, either directly or indirectly:

Thin-film or wound heater: This is by far the most common approach.
Initially, the tube is heated to a temperature sufficiently above where it
would reach thermal equilibrium from bore heating alone. How high this is
set is a tradeoff betwen operation over an acceptable ambient temperature
range and a laser that runs excessively hot. Then heater power
can be used to balance convection cooling such that the tube temperature and
actual cavity length are maintained constant based on mode feedback. The
heater power at the operating point is typically 1/4 to 1/2 of the bore
discharge power.

Thin-film (Kapton) heaters are available from several manufacturers in a
large variety of configurations, but may also be customized (at possibly
significant expense) in terms of size, resistance, and temperature coefficient
of resistance (which enables the actual resistance to be used to determine
the tube temperature without a separate sensor). Thin-film heaters usually
have an adhesive backing such that installation is very simple.

Wound heaters may be implemented using an appropriate size and length
of copper "magnet" wire wound "bifilar style" to minimize the magnetic
field produced by the heater current. This is more labor-intensive but
acceptable for prototype or small production runs.

Induction heater: Since the mirror mount stems on modern HeNe
laser tubes are made of metal, it is possible to couple energy into them
via a small coil driven with a low power high frequency source, which
can then be regulated to maintain the cavity length constant. This was
pioneered by Aerotech in the Syncrolase S100, adapted by Melles Griot in
the 05-STP-909/910/911/912. The thermal time constant of the mirror mount
step is much smaller than that of the glass tube so response is better.
However, with only a limited length available, it can be tricky to
assure that lock will be maintained as other parts of the tube expand.
One benefit of this approach is that *any* HeNe laser tube of suitable
length where a coil can be fit can be stabilized.

Bore heat/fan: This rather peculiar approach is to the best of
our knowledge has only been used by Teletrac on some of the early stabilized
HeNes. Some might call it a kludge, but it actually works remarkably well.
Initial heating is provided by both
the HeNe bore discharge and a couple of small light bulbs near the tube. Once
a temperature set-point has been reached, the light bulbs are turned off
(and not used while the tube is locked) and a low vibration PZT fan provides
active cooling. The PZT fan is just a pair of blades that vibrate with
variable amplitude based on the mode feedback - getting really excited when
cooling will pull the desired mode into position. :) One advantage of
this approach is that with active cooling (even if it is wimpy), the
laser can run at a lower temperature closer to ambient than with heat-only.
A disadvantage is that even though designed to minimize vibration, the
PZT fan is not perfect. And even miniscule vibration can be an issue
for interferometer-based devices.

ThermoElectric Cooler (TEC): In principle, a TEC (which can
actually both cool and heat) could be used to control cavity length.
However, since these are usually planar devices, adapting them to a
cylindrical tube could prove challenging. This would require an adapter
made of a high heat conductivity material. And even then, the thermal
delay could make stabilization impossible. It might be possible to do
this on one of the mirror mount stems though.

PieZo Transducer (PZT): A PZT can provide movement over a small
range which can be sufficient for cavity length control under the right
conditions. Early Hewlett Packard (HP) metrology lasers
(5500A/B/C and 5501A) used a PZT between the mirror spacing rod
and the cathode-end mirror *inside* the tube envelope. So it
would move the mirror directly by just enough displacement
to cover a sufficient range to guarantee a suitable lock point.
However, even though the mirror spacing rod (which along
with the PZT determined the cavity length) was made of ZeroDur™,
after awhile, the cavity length could still drift out of range and the
lock-point might have to be reset. Later HP lasers (to the present)
use a resistance heater, but it is still inside the tube.

Where the tube structure that defines the cavity length is not made
of a material like ZeroDur™, it would be difficult to use a
PZT because the overall length would be changing by orders of magnitude
more than a common PZT could accommodate. At the very least, the
laser would have to use active temperature control and
warm up for hours to reach thermal equilibrium
before the feedback loop could be closed using the PZT. This is how
the Spectra-Physics 119 laser was implemented.

However, PZTs can easily provide dither and have been used for this purpose
in several iodine stabiilized HeNe lasers built by NIST and Frazier, among
others.

Electro-mechanical: Finally, glass and metal are elastic on
the micro-scale. So, in principle, an external electro-magnetic actuator
like a common solenoid can push or pull on one of the mirror mount stems
and actually squeeze or stretch the tube enough to control the cavity
length. It's order of pounds to cover a few microns. We are not aware of any
commercial stabilized HeNes using this approach for cavity length
control, but at least one (Spindler and Hoyer) did use it for dithering.

In actually designing a practical stabilized HeNe, there are several functions
that need to be performed regardless of how it is actually locked:

Turn on the laser tube and detect that it lights with adequate power.

For thermally controlled lasers, warm up the tube to the desired
operating point.

Lock the laser to the reference (intrinsic or estrinsic).

Detect loss of lock or inability to lock, loss of beam, etc.

For a very basic implementation, (1), (2), and (4) can be done manually,
though most systems use either a temperature sensor, some type of timing
of mode sweep, or simply a fixed delay to determine when the laser is
ready. Actual locking (3) may use a variety of electronics from simple
to complex, a microprocessor, or a combination of the two.

Before the availability of inexpensive microprocessors in
the early 1980s or thereabouts, controller implementation consisted of
TTL or CMOS ICs for logic and timing along with op-amps for the actual
feedback loop. (Or discrete transistors or vacuum tubes before that!)
These were effective, inexpensive, and easy to repair
should the need arise. But as time went on, the parts
that were used have become harder to find. At least one company, Agilent,
came up with an intermediate solution using a Field Programmable Gate
Array (FPGA) that essentially replicated a large portion of the
discrete logic in a single chip. And engineers
just can't resist redesigning perfectly satisfactory systems. ;-)
Nowadays, a dirt-cheap single chip microprocessor or microcontroller
(same thing) is the solution of choice, with at most a few analog
parts to condition the input signals.

So, most stabilized HeNe lasers that are not legacy products from the 1980s or
before use a microprocessor to perform most logic, timing, testing, and
control functions, though some may use a purely analog implementation for
actual locking using the feedback loop to reduce noise in the control
signals that could end up modulating the optical frequency. For most
users, this is not a problem. But as an example,
the Melles Griot 05-STP-901 and functionally identical Spectra-Physics
117A which date from the early 1980s or before
used Pulse Width Modulation - PWM - to drive the heater wrapped
around the tube. (Many modern microprocessor-based implementations
including µSLC1 use PWM as well.) Very finicky users have
detected the residual ~5 kHz PWM
in the laser's optical frequency and complained. This would probably
only show up if the output of a laser like this were beat - combined
so that a difference frequency could be detected - with the output
of another laser and the result displayed on an RF spectrum analyzer
or similar instrument. A trivial change to the electronics can
convert the PWM to a purely linear control loop. With a microprocessor,
switching to a Digital to Analog (D/A) output instead of PWM would also
greatly reduce digital noise in the feedback loop.

The benefits to the user of a microprocessor-based controller are in
flexibility, reliability, and cost. The benefits for the manufacturer
also include the system now being proprietary - user
repair, among other things, is virtually impossible because
the smarts are in the software/firmware,
which is generally not made available to anyone outside the company or
their authorized service organization. If a TL084 op-amp
went belly-up in an SP-117A, basic troubleshooting techniques could
be used to repair it. Or if the laser tube required replacing, there
were three trim-pots to perform all adjustments. With a similar modern
laser, repair of all but the most obvious problems like a bad DC
power supply or blown fuse is virtually impossible. In some cases,
replacing the tube requires access to firmware parameters to set
various constants. Even identical model HeNe laser tubes (assuming one
is avilable) may differ in the output power of the waste beam from the
back of the tube - which is often used for the feedback.
There may be workarounds by adding a PCB with
adjustable op-amp circuits to fake the signals derived
from the tube to match what the firmware expects, but these are not
ideal solutions. There is a silver lining for the user though - it's
impossible to break anything by opening the
case and twiddling adjustments because there are none. (Although
that's not always strictly the case, as with µSLC1 where
the coarse mode gain adjustments are trim-pots!)

Having said all that, any new stabilized HeNe IS going to use a
microprocessor for the bulk of the controller, with perhaps an
analog section for the actual feedback loop. Being able to tune
the control loop by changing parameters rather than soldering
components or even adjusting trim-pots is just far superior for
development and maintenance. However, there will then generally
be NO User Serviceable Parts inside. ;-)

Aside from the effects on the physical dimensions of the tube, the center
of the NGC depends on the gas temperature and pressure, and ambient/tube
temperature affects the internal pressure directly as well as from changes
to the tube structure.

Under normal conditions, the changes in internal pressure are likely to be
much less than 1 Torr and temperature itself has only a small affect on the
gain center. The major one is gas fill ratio of
22Ne:20Ne. This is of course determined at the
time of manufacture (and may not be that accurate), but will also decline
slightly with use as 22Ne will be trapped at a slightly a higher
rate than 20Ne.

One way to assure that the tube itself runs at a relatively fixed known
temperature is to warm it up to a set-point temperature rather than using
an indirect method like the rate of mode sweep to determine when to lock.
And then to fine tune that after awhile to give everything time to reach
thermal equilibrium. Once locked in this manner, the temperature of the
tube will remain relatively constant. To improve it even further,
at least two companies (Lab for Science and MicroG) put the tube (with its
heater wrap) in a temperature-controlled housing. Most do not.

Intrinsic Stabilization Techniques

While the laser tubes used in many very expensive stabilized HeNe lasers may
be virtually identical to those that used to be found in grocery store
barcode scanners, one cannot take any old tube found on the street and
expect it to be usable in a stabilized laser. Many parameters affect
performance.

Most of the following requirements are common to all of the intrinsic
stabilization techniques. Any specific ones will be noted.

Single spatial mode (TEM00): This is determined by the geometry
of the laser tube structure (mostly the cavity length, mirror
curvature, and bore diameter).

Nearly all red HeNe laser tubes are specified to be TEM00 since most
applications require that they be single spatial mode.

Single longitudinal mode when locked: Depending on the locking
technique, the raw output may be more than 1 mode, but for
random polarized tubes, a polarizer can be used to block the
unwanted mode(s). In principle, a tube with a
cavity length of up to around 350 mm could satisfy this requirement if one
mode is centered on the neon gain curve. Then, the two on each side could
be blocked because they will have orthogonal polarization. However, locking
to the peak becomes more complex and longer tubes tend to be less stable
due to mode competition. In addition, due to the laser dynamics,
where more than two modes are present, none of the modes are a pure
single frequency as is possible with only two modes present.
So few commercial stabilized HeNe lasers use
tubes longer than about 250 mm, where only two modes are present when
locked, one of which is removed by a polarizer at the output.

Very short tubes may be locked with single mode output over a modest range
even if they are not random polarized. Some older lasers used tubes with
Brewster windows, which are inherently polarized. But techniques like Lamb
Dip and gain peak locking can still be effective, as well as simple intensity
locking. However, modern stabilized HeNe lasers using intensity locking
are likely to use short random polarized tubes.

Mode behavior: The major consideration is that the polarized modes
be consistent - adjacent modes must be orthogonally polarized, their
orientation should not change over the life of the tube, and the
polarization must not "flip" at random as the laser cavity expands or
contracts with temperature.

Unless the tube manufacturer guarantees a specific model tube is well
behaved, it must be tested prior to use in a stabilized laser.

Fortunately, Murphy must have taken a day off for the red HeNe laser.
Due to non-linear aspects of mode competition, adjacent modes in the red (633
nm) random polarized HeNe laser are nearly always orthogonally polarized.
This is not generally true by default for other HeNe wavelengths, though
it can sometimes be forced with a weak magnetic field or by other means,
but such techniques can be tricky and unreliable. Since the 633 nm
wavelength is capable of the higher power, obeying this rule is
fortunate. It would have been nice though if Murphy hadn't been
so selective. ;-)

Some model tubes are spec'd to be "non-flippers" or have "non-mode flip
optics". For some manufacturers, this really means testing and selecting
those tubes that qualify. Others have the manufacturing process controlled
well enough to guarantee it without sorting. And one company (REO) has
a patented funky resonator mirror configuration for this purpose
(but even they don't always get it quite right).
If not a part of the tube specification, then some samples may be suitable
but not all. However, if a tube tests as a non-flipper over the temperature
range where it is being used, it will probably be satisfactory as this
behavior doesn't tend to change with use. But some tubes start out as
flippers when cold and then settle down after warmup, which would be
acceptable. And with clever design, even many flippers can be used
in stabilized lasers as long as they can be locked at a point away
from where they flip.
Of course, as an end-user of tubes, testing tubes and having to throw
away a large percentage of unsuitable expensive tubes could be a
strain on job security. :)

Free of rogue wavelengths: While not very common, some red
(633 nm) HeNe laser tubes produce a low level output at one or more
other wavelengths, most commonly 640.1 nm (deeper red). This is really
only likely in longer tubes - over 5 mW. It's easy to test for with
a diffraction grating. A compact disc works fine for this. There
should only be a single diffracted spot corresponding to 633 nm.

Tubes suitable for any of the stabilization techniques are usually short
enough that rogue wavelengths are extremely unlikely.

Where multiple modes are present when the laser is locked, all of them may
be used as output. Specifically where 2 modes are present, the laser may be
set up to produce a beam with two optical frequencies separated by
approximately the longitudinal mode spacing of the laser tube simply
by not blocking one of them. Since
the locking techniques do not change for these, they are not coveered
separately.

In the grand scheme of things, common mass produced internal mirror HeNe
laser tubes are darn good without requiring any fancy stabilization.
They have a typical coherence length of a few inches and an absolute
optical frequency accuracy of around 2 to 3 ppm. For many applications,
even high precision ones including interferometry where the path length
difference is small or holography of small objects, these are more than
good enough. And we have the NGC to thank for it all. ;-) Thus, before
committing to a much more expensive stabilized HeNe laser, a determination
needs to be made of the actual requirements. And aside from lower cost,
unstabilized HeNes are generally capable of much higher power.

In the chart above, there is an entry for multiple transverse mode (non-TEM00)
lasers. While technically, the lasing modes are all within the NGC and thus
limited to a gain bandwidth of 1.5 or 1.6 GHz and thus around 3 ppm, as a
practical matter, their relative optical frequencies is for all intents and
purposes, unpredictable. So, using such a laser as a reference for anything
could be....interesting. Thus, there are no values given for the optical
frequency variation or accuracy.

For the unstabilized single transverse mode laser - which describes most
red HeNe lasers that aren't stabilized - there will be multiple longitudinal
modes but they will be separated by approximately the cavity FSR or c/2L.
Coherence length (or period) is thus predictable, if short compared to
single longitudinal mode stabilized lasers. However, as the length of the
tube and output power increases, the modes become much less well behaved
due to mode competition. The relative amplitudes of the modes tends to
change at random with only loose regard for the profile of the NGC.

It is possible to stabilize a HeNe laser by simply controlling its
environment, mainly temperature. Of course, that will generally require
some feedback of its own, but not of the laser tube specifically. One
of the earliest stabilized HeNe lasers - the Spectra-Physics 119 - was
available both with and without the "Servo Option". Without it,
stabilization was strictly based on setting the temperaturee of the
tube enclosure. With a sufficiently long warmup of a few hours (!!) this
was effective reducing the uncertainly in optical frequency from the
width of the NGC (1.5 to 1.6 GHz) to around 75 MHz - a reduction by a
factor of 20 or more to below 0.15 parts per million (ppm). But with
the Servo Option, which provided Lamp Dip stabilization (see the section
below) uncertainty dropped to 5 MHz or 10 parts per billion (ppb).

While there is no active feedback based on the NGC, a human must set the
mode position based on the NGC, so it is still intrinsic. ;-)

Any HeNe laser tube suitable for a stabilized HeNe laser can be controlled
in this manner. Depending on tube size, a 1 °C change in tube temperature
will change the mode position by a few hundred MHz or more due to the
change in distance between the mirrors. So temperature
control is required to a small fraction of a degree. But this
is not difficult even with the electronics that was available in the 1960s.

However, to truly reduce the uncertainty so as not to require the user
to fiddle with the thing, some form of optical feedback is needed.

A random polarized tube is generally used since over a large portion of
mode sweep, even a relatively short tube will actually produce 2 modes.
For use with random polarized tubes, a polarizing beam splitter blocks
the unwanted mode and a non-polarizing beam sampler diverts a small portion
of the output beam to a photodiode to be used for locking feedback.
Or if both modes are desired in the output, the mode used for feedback
can be diverted using a beam sampler, or taken from the waste beam at
the back of the laser.

To provide the ability to move the lock point over a large portion of the
LOPC with no possibility of a third mode popping up, the tube must have
a cavity length of less than about 200 mm.

Short polarized tubes could also be intensity-locked, though it's not
clear why this would be desirable: There is no advantage to using
a polarized tube in a single frequency laser with a serious limitation
in output power since the tube has to be short enough so that only a
single mode is lasing when locked as the unwanted mode cannot be removed
with a polarizer.

The only purely single mode stabilized HeNes I am aware of are the Aerotech
S100 which morphed into the Melles Griot 05-STP-91x series. These are NOT
microprocessor controlled. ;-) Although newer versions of this laser
actually have hooks in place to
support conversion to a dual mode stabilized laser by adding a photodiode
and changing a jumper, this is not publicized. :) The 05-STP-91x lasers
lock on the side of the LOPC using a novel induction heating approach
originally developed by Aerotech. This is compact and allows for fast
time-to-lock, but the more conventional heater wrap can also be used.
More info on these lasers may be found in the section:
Aerotech Stabilized HeNe Lasers.

Most dual mode stabilized HeNe lasers have a user selectable option
(switch, jumper, or logic input) to lock to a single mode. These are
described below.

Dual mode polarization stabilization uses the relative amplitudes of the
two polarizations from the laser tube for locking. See
Dual-Mode Single-Frequency Stabilized HeNe Laser.
For frequency stabilization, they are
generally forced to be equal and thus parked equidistant on either side of
the LOPC. However, their relative position can be changed (slowly)
over a modest range if desired. This is usually done by a knob, an
external modulation signal, or a software command.
A polarizer can block the unwanted mode because they are
orthogonally polarized. Or, the laser may be used with both modes thus
outputting two frequencies separated by the tube's longitudinal mode spacing.
The diagram shows a purely analog electronic implementation of the
controller, but most modern systems use a microcontroller to implement the
locking algorithm. An example is shown in
Single or Dual Mode Polarization Stabilized HeNe Laser using uSLC1d1.gif Controller.

Dual mode polarization is by far the most popular technique
used in commercial stabilized HeNe lasers at the present time.
It is also the only common approach offering the highest power
in a pure single longitudinal mode (single optical frequency).
With a lively tube, this can be
2 mW or more in a single mode when the modes are balanced.
For greater power, they can be offset
somewhat with either frequency or intensity stabilization providing
up to 2.25 mW or even more in a pure single mode.
(However, 1.5 mW and 1.75 mW, respectively, are more typical
in stock tubes unless specifically selected for high power.)
The limiting factor
is either where a third mode appears, or where the output mode
approaches the center of the NGC. To get higher power without fancy
and expensive additional complexity like an intra-cavity tuned
etalon requires going to three mode stabilization. But then the output
mode is never quite pure regardless of locking technique.
For many applications a few percent of unwanted amplitude
or frequency modulation may be acceptable.

Laboratory lasers using dual mode polarization stabilization
often also have optional intensity stabilization selected by a switch, logic
level, jumper, or software, where one of the modes is locked
to a reference level rather than the two modes being compared.
A means of changing the reference level may also be provided.
There will still be only a single mode present (when
the other one is blocked) over a fairly wide range of optical frequencies on
either side of the point where the two modes are equal so that the output
intensity can be adjusted up or down. Specifically, with intensity
stabilization, it may be set up to output somewhat higher power.

The tradeoff is that the optical frequency accuracy and stability is
better when both modes are used, but at the expense of intensity stability.
But the intensity stability is better using the single mode.

Three mode stabilization can provide just about the highest
power possible in a stabilized HeNe laser using an off-the-shelf internal
mirror laser tube. This can be double or more compared to the
typical 1.5 mW of commercial dual polarization stabilized lasers.

However, it is not without drawbacks. These are related to mode purity
and long term absolute frequency drift.
When three modes are lasing in a HeNe tube, there will also be three
relatively weak "ghost" modes very close to the lasing modes.
There are caused by third order non-linear dynamics. The
difference in optical frequency between the ghost modes and lasing
modes of a up to a few hundred kHz is exploited by second
order beat stabilization for locking (but not for the other techniques).
There is no practical way to remove the ghost mode associated with the
centered (main) mode from the output.
So, strictly speaking, the output of these lasers is not truly pure
single mode. In addition, to maximize output power, it's possible
that some tubes may have small 4th and 5th normal lasing modes present
400 to 500 MHz from the closest desired lasing modes. Both of
these are typically under 5 percent of the amplitude of the output,
which could be acceptable for many applications. Two mode stabilization
does not suffer from either of these issues except during warmup
when three modes may be present during part of mode sweep. This is
generally of no consequence to the ultimate application unless the
laser is used during this period. So these two potential issues
should be kept in mind in determining if the increased
output power provided by the three mode techniques outweighs the
presence of extra low level modes.

A well behaved random polarized single transverse mode (TEMOO)
HeNe laser tube 13 to 14 inches in length can
provide 3 to 4 mW in a nearly pure single mode if it is centered on
the LOPC. (As above, "well behaved" means that adjacent modes are
orthogonally polarized and it is a non-flipper.)
Two modes of the opposite polarization will straddle it and can be blocked
in the output beam with a polarizer. Ideally, there will not be any other
modes present. The next two ones would be just beyond the tails of the
NGC. However, if the tube is very lively or a bit too long, they may poke
their heads up and result in weak rogue modes that cannot be eliminated
because they will have the same polarization as the desired centered mode.
If the tube is shorter, those weak modes can be guaranteed to
disappear entirely, but with a sacrifice in output power. So, it's a
tradeoff of output in the dominant mode versus the rogue weak ones. For
many applications, a few percent in modes almost 1 GHz or more away from the
dominant made is acceptable. However, for some stabilization techniques, the
additional modes, even though weak, may introduce noise in the locking signal.
The ramafication so of this are left as an exercise for the student.

Suitable tubes for three Mode stabilized laser should include the Melles Griot
05-LHR-150, Siemens/LASOS LGR-7627, and JDSU 1125 as long as they are confirmed
to have well behaved modes - they are not bouncing around due to mode
competition and are not-flipping polarization. Nearly all red (633 nm)
HeNes satisfy the requirement for adjacent modes to be orthogonally polarized.
All three types should be available new or surplus. The older Aerotech OEM5R
may also be suitable. These are all rated 5 mW but new samples may have
much more power output up to 8 mW or more.

Three approches to three mode stabilization are discussed below. The
simplest one overall is probably second order beat stabilization and has
the potential to provide the best optical frequency stability.

But whether it is worth going to any of these more complex, more expensive, and
physically larger schemes for a benefit of few tenths of a mW will depend on
the application. As a practical matter, to guarantee that the rogue mode
amplitude will be minimal, at most 3.5 mW will be available in a
single (mostly) pure mode. And to accomodate variations in tube
performances, it may be closer to 3.0 mW. Consider that the slightly
shorter tubes for dual mode polarization stabilization can be spec'd
to 4 mW or more. I've measured output power from tubes that were not
brand new as high as 4.5 mW. But even at 4.0 mW, the balanced lock
point would be 2.0 mW. And by offsetting the lock point slightly,
2.25 mW or even slightly greater power may be available in a single pure
mode with a simpler more conventional system.

In addition, when designed for maximum power, there will be little to no
tunability of optical frequency - the output mode MUST be centered on the
NGC. Where tunability is a requirement, three mode stabilization
can still be used, but maximum output power will be somewhat lower,
and will vary with the lock point. However, it will then provide
higher power from a tube otherwise suitable for dual mode stabilization
since the region at the peak of the NGC will be usable.

This is a relatively simple implementation as shown in
HeNe Laser Using
Second Order Beat Frequency Stabilization. It may also be capable of
the highest stability of any of the intrinsic techniques, at least short
term, though this is not really known. But the same considerations with
respect to additional complexity, size, and cost discussed above will apply.

The HeNe laser tube requirements are basically as discussed above, where
(ideally) at most 3 modes can oscillate when one of them is centered on
the NGC. In the diagram, the tube length is such that
this requirement is met. If one is willing
to accept a small amount of output on the two additional modes that would
be present with a slightly longer tube, or one that is livelier, then a
bit more power in the centered mode may be possible. However, the rogue
modes will result in additional low level beat signals which may result in
locking problems. Thus, assuring the tube is pure 3 modes is desirable, at
least until the basic design has been tested. This can be often be
accomplished on a lively or slighty too long tube with little loss
of power by carefully slightly misaligning the OC mirror.

When a HeNe laser is oscillating with three longitudinal modes, there will
be primary difference frequencies corresponding to the distances between
the lasing modes, and secondary difference frequencies between
pairs of primaries. While the primary difference frequencies differ by
approximately the longitudinal mode spacing of 400 to 500 MHz for this
length tube, the secondary difference frequencies are in the hundreds of
kHz range and easily detected and used as the locking variable. Note
that if there are rogue 4th and 5th modes oscillating, there may be
other primary, secondary, and tertiary difference frequencies to contend with.

"When nearly symmetric in the HeNe gain profile, the three mode
laser contains three additional low power modes. The three
additional smaller modes arise from third-order non-linear harmonics
and their exact frequency difference with respect to their
nearest adjacent mode depends on cavity tuning and the excitation
state of the active medium. In this work, the frequency
difference between a smaller mode and its main mode,
vb, ranged
between 200 kHz and 550 kHz. The three main modes from lowest
frequency to highest are v1, v2,
and v3 and the three smaller mode frequencies are
(2v2-v3),
(v1+v2-v3), and
(2v2-v1). Alternative expressions
for the three smaller modes are (v1+vb),
(v2-vb), and
(v3+vb), respectively."

Since the frequency of (v2-vb)
will be in the range of hundreds of kHz and a strong function of
center mode position on the NGC, it can be used for locking.

The only known commercial stabilized HeNe laser that is known to have
employed the Second Order Beat (SOB)
locking technique was the Laboratory for Science 260. Only about 10
of these were ever manufactured and can you believe it, I have not seen
a single sample. :( :) The LFS-260 dates from the late 1980s or early 1990s
and used a Phase Locked Loop (PLL) IC to lock the beat to a
crystal controlled frequency synthesizer. This still may be the
approach with the best precision and stability, but nowadays a
microprocessor can do almost as good a job with much more flexibility.
I suppose LFS didn't publish to (1) keep the technology proprietary and
(2) so others wouldn't think they were nutcases. :)

Here is the theory of operation from the LFS-260 brochure:

"In a laser with three TEM00 modes, there will be two primary beat
frequencies corresponding to the difference frequencies between the
central mode and each of the modes on either side of center. These two
beat frequencies, typically in the range of 400 to 500 MHz, will in
general not be exactly the same because the frequency pulling effects
on each mode will vary with the differing slopes at the respective
operating points on the Doppler gain curve. The difference between
these two beat frequencies will yield a third or intercombinational
beat frequency typically in the range of 100 kHz. In an integral end
mirror tube, where the alternate modes are orthogonally polarized, the
intercombinational beat frequency will not be zero even when the
central mode is at line center because of the birefringence of the
mirrors. In the Model 260, the laser tube is preselected not only for
power but also for an appropriate range in the intercombinational beat
frequency. The median frequency is then tightly phase locked to the
frequency of a crystal controlled frequency synthesizer. "

In HeNe Laser Using Second Order Beat Frequency
Stabilization, the tube length is such that only three modes can oscillate
when one of them is centered on the NGC. If one is willing to accept a
small amount of output on the two additional modes that would be present
with a slightly longer tube, or one that is livelier, then a bit more
power in the centered mode would be possible.

The Black Hole is supposed to capture every last photon of the undesired
modes. (LFS called their version a "black etalon", but I think black hole
better captures the spirit of its function.)
However, something more easily obtained will suffice, just as
long as it doesn't reflect back into the laser. ;-)

The above paper uses a photodetector sampling the output polarization
to obtain the beat signal for use in locking. In my initial tests using
a Melles Griot 05-LHR-150 tube,
there was a strong beat present at the lock point when taken from both
the output polarization (centered mode) and blocked polarization (outer
modes). So it may also be possible to use the blocked polarization
since it contains the outer modes.
In that case, the Black Hole would need to be moved to after
the beam sampler. I hope it doesn't weigh too much. :)
However, the paper suggests that this
may have more non-linearities in the locking signal.
There's a lot going on here, some of which may not be intuitively obvious.

The exact beat frequency where the lasing mode is centered
is not the same for each tube sample due to differences in parameters like
mirror birefringence and orientation, this would need to be tested and entered
as a constant into the firmware or PLL synthesizer. The correspondance of
lock frequency to aboluste optical frequency depends on many factors.
While LFS claims locking parameters in the model 260 don't change much.
this may not be entirely true. For example, the lock point for the same
absolute optical frequency is a strong function of tube (gas) temperature
and pressure. So the exact lock temperature and tube aging will affect them.
And maintaining the same optical frequency may impact the output power if
it moves off from center on the NGC.

The locking variable is the second order beat frequency. This typically a
few hundred kHz in amplitude modulation depth of between 0.5 and 5 percent
of the power in the centered mode. Extracting it and converting to a
TTL signal is not entirely trivial, expecially where it is desired to
minimize reduction in the usable output power. Ideally, it should be
taken from the waste beam which has a typical single mode power of only
around 25 µW, resulting in a DC photodiode current of around 10 µA
and an AC signal of under 1 nA. The detector circuit would require careful
analog design using low noise construction techniques. For my prototype,
I am sampling the output beam with a glass plate and using an HP/Agilent
10780A, which has barely enough sesitivity even with the 300 µW
available there. It would not work at all using the waste beam. (The
10780 has no problem with under 10 µW when used in its normal
application with HP/Agilent two frequency HeNe lasers, but then the
useful signal is 25 to 50 percent of the total power, not under
5 percent or less.)

In addition, any ripple in the HeNe laser power supply also modulates
the amplitude of the laser's output, and it may have
similar or greater AC amplitude as the second order beat.
If the DC current is set optimally, the dominant contribution of the
ripple frequency will be at twice the power supply switching frequency.
In tests, it was necessary to add
an external ripple reducer to the standard Melles Griot 05-LPL-902 power
supply for the 05-LHR-150 laser tube and another
stage might be desirable. While the typical switching frequency is
below the expected beat frequency and the optical receiver can filter
this to some extent, strong harmonics will still be present, especially
that second harmonic. A fully analog supply would be suprior with
additional filtering of both the DC rail (to eliminate ripple at the
AC line frequency and its harmonics) and ripple reduction in the
output (to suppress zener noise/plasma oscillation ripple).

The controller would need to warmup the tube as with other more mundane
locking techniques, and then use the a value derived from the difference
between the reference value and actual second order beat to drive the heater.
Since the relation of beat frequency to mode position and absolute optical
frequency is a strong function of tube conditiona (internal temperature
and pressure), it may be best to use tube temperature to determine when
to turn on locking, rather than some measure of mode sweep rate or count.

I am in the process of building a system of this type using a variation on the
µSLC1 controller, µSLC2. A diagram is shown in
in Three Mode HeNe Laser Using Second Order Beat
Stabilization and a photo in Prototype
Three Mode Stabilized HeNe Hardware with µSLC2. This provides
both the P and S mode signals from the back of the tube and the beat signal
using a modified HP 10780A optical receiver sampling the output beam.
Using the output beam was done out of convenience since even sampling only
10 percent of it has much higher power than the waste beam and even then,
the 10780A is barely sensitive enough.

Stay tuned.

To summarize some of the major issues:

While the beat in the few hundred kHz range is used for locking, it will
also be present in the output of the laser as a low level amplitude
modulation or ripple, which cannot be removed. So strictly speaking, this
type of stabilized HeNe laser is NOT pure single longitudinal mode or single
frequency even without any rogue 4th and 5th modes present. The impurity is
probably between 0.5 and 5 percent of the total power. The same would
be true of ANY HeNe with 3 or more longitudinal modes present from the tube,
not only those using second order beat stabilization.

Since the beam detector looks at amplitude modulation of the output,
the HeNe laser power supply will need to be a very low noise unit.
Preferably this would be fully linear, but that would probably mean
a custom design as virtually all modern HeNe laser power supplies
are switchmode. These operate in the 20-100 kHz range with harmonics
similar to the relevant frequencies for the beat signal. More than one
stage of ripple reduction on the output may be required.

According to the paper, it appears as though the operating temperature
critically affects the beat-versus-optical frequency/location on the neon
gain curve. Therefore, it may be necessary to add a temperature sensor to
the tube and warmup to a specific temperature rather than going by mode
sweep cycle time to determine when to lock.

It's not clear how tube use/aging will affect behavior since this also
results in changes to the gas pressure/temperature of the tube. So it is
not known if these can be a "set and forget" type system or whether they would
require periodic tuning and/or whether this can be automatically performed
by the controller firmware.

Each system will need to be set up and tuned for the specific tube
used. It's not known if all samples of tubes of the same model will even
be satisfactory in terms of beat range and behavior since the manufacturer
is not going to test the relevant parameters and is usually optimizing
for total power.

Although the paper claims 3.5 mW, it is not known whether this is realistic
in a production system. Hopefully the manufacturer will be able to tweak
the design for maximum power in the main mode but at low volume, this may
not be realistic.

So there's a lot going on here compared to the traditional dual mode laser.
(Much of this applies to any three mode laser, not only one using second
order beat stabilization.)

It may also be possible to use the amplitudes of the polarized modes to lock.

However, (1) the modes do not
change in amplitude by very much - perhaps 5 to 10 percent of the total power
and (2) the lock point will NOT be where their amplitudes
cross as with the dual mode
stabilization, but rather where one is maximum and the other is minimum,
and they are nearly constant in these locations.
Therefore, a simple comparator cannot be used. Rather a technique
that locks to the peak or valley of a function of the mode signals is
required. One is called Pound-Drever-Hall locking. Essentially, the cavity
length is periodically dithered by a small amount and the laser is
locked to a zero crossing of the 2nd harmonic of the mode signal.
This sounds hairier than it is. A microprocessor can do it in
real-time and electronic systems and even ICs exist for various
applications. They are called "lock-in
amplifiers", "synchronous demodulators", or "phase sensitive
detectors.

As noted, a microprocessor can also implement PDH locking.
For something inexpensive like the Atmega Nano 3.0 used in µSLC1,
the dither frequency would need to be limited to a few hundred Hz.
Although dither frequencies of a few kHz have typically been used,
this should be adequate.

Hardware is similar to that of seond order locking, but with no
need for the beat detector. A photodiode is needed to monitor
one of the polarized mode amplitudes to be used as the PDH variable,
but monitoring both will provide double the signal-noise-ratio.
There would also need to be
some means of dithering the cavity. A suitably designed heater may
have enough bandwidth if driven with a high level AC signal on top of the
one for maintaining cavity length, but if not, then an electromagnetic
(voice coil or solenoid) could be attached to act on one of the mirror
mount stems. This dither will show up in the output as modulation of
the optical frequency (along with the second order beat signal).

It's not likely that PDH locking would provide any real advantage compared
to either of the other approaches and using the second order beat is
probably simpler.

The tube requirements for two-frequency axial Zeeman lasers are very similar
to those for non-Zeeman stabilized HeNe lasers but not identical:

Single spatial mode (TEM00): This is determined by the geometry
of the laser tube structure (mostly the cavity length, mirror
curvature, and bore diameter).

Nearly all red HeNe laser tubes are specified to be TEM00 since most
applications require that they be single spatial mode.

Single split longitudinal mode when locked in Zeeman magnet:
Since the magnetic field splits the neon gain curve and spreads the two
halves apart, the effective gain bandwidth is increased significantly.
Thus the length requirements for axial Zeeman lasers is substantially
more stringent. In addition, unlike the single frequency laser,
it's not possible to block unwanted modes because both polarization
orientations are required in the output. Thus, only a single split
mode can be present when locked.

Depending on the strength of the magnetic field, most practical lasers
require the cavity length to be limited to 125 mm (~5 inches) or less.
Otherwise, "rogue modes" may be present which can result in problems in an
interferometer and/or prevent locking at all. And even shorter tubes
provide more flexibility in selecting the "split" or REF frequency,
but they suffer from lower power. Nonetheless, tubes with cavity lengths as
short as 81 mm (~3.2 inches) have been used in commercial axial Zeeman
lasers with acceptable output power, specifically the Zygo 7705. And
a 102 mm (~4 inch) cavity length is used in current production Keysight
5517 lasers.

Mode behavior: Being a non-flipper is actually NOT a
requirement for axial Zeeman HeNe lasers. In fact, it's the
exact opposite: Tubes that flip or change polarization at random are
often better candidates because the tendency to specific polarization
axes won't fight the magnetic field, which is forcing circular polarization.
A tube that is optimal for a single frequency HeNe laser may make a poor
axial Zeeman laser requiring a higher magnetic field, having an unstable
beat, or not producing a beat at all regardless of magnetic field strength.

HP/Agilent/Keysight tubes tend to have quite random mode behavior without
a magnetic field. However, common barcode scanner HeNe tubes which may
have well behaved polarization can sometimes be used, though those that
are flippers tend to be better. At least one company now manufacturs
a series of tubes suitable for use as replacements for the
tubes in HP/Agilent/Keysight lasers.

Nearly all the two-frequency HeNe lasers used to position wafers
in multi-multi-million dollar semiconductor Fabs and other super high
precision metrology applications use dual mode polarization
stabilization. See Dual-Mode Stabilized Axial
Zeeman-Split Dual-Frequency HeNe Laser, which can also, of course
use microprocessor as in µSLC1. The shape of the NGC/LOPC differs
due to mode competition of the short tube in its axial Zeeman magnetic field,
but locking is similar. And non-Zeeman two-frequency lasers such as
those from Zygo also use dual mode polarization stabilization.

There are a few variations. Most HP/Agilent/Keysight lasers use a clever
implementation with a single photodiode behind an LCD polarization
rotator and polarizing filter that alternately samples the H and V
polarized modes. Sample-and-hold circuits capture the values and
these are what are used to control the feedback loop. This approach is
largely immune to drift in the electronics over the life of the laser tube.
The Spindler and Hoywer ZL-150 is the only known axial Zeeman laser that
does not use dual mode polarization stabilization, but rather mechanically
dithers the laser tube cavity length and locks to the point where the
split frequency is a maximum.

Note that locking to a specific split frequency using a PLL or similar
technique is generally NOT recommended as its exact value depends on
many factors including the power output of the tube and local magnetic
fields. As the tube ages with use, power output generally declines
and the splite frequency increases. Any external magnetic fields - even
the magnetized base of an optics mount or another similar Zeeman laser -
will change the split frequency. So, the laser may not remain at the
center of the split gain curves as desired.

The transverse Zeeman HeNe has to potential to produce truly high power
(at least for this sort of laser), in a split single mode than
any of the others discussed so far. When a transverse magnetic field
is applied to a random polarized HeNe operating with 3 modes with one centered
(as in the three mode lasers described above), if the field
strength is such that the Zeeman shift is the same as the cavity mode
spacing, it is possible for the modes on the sides to be suppressed with
all the power collapsing into the main center cavity mode. Up to 5 mW or more
may be possible with this scheme. The required field strength should be
on the order of c/2L/2.8 G, or around 150 G for a typical 5 mW tube with
a cavity length of 350 cm.

However, there is, as always, a catch. ;-) Although the papers talk about
a single mode, it's actually a pair of closely-spaced H and V compoennts
using the same cavity mode, similar to the axial Zeeman laser but generally
with a much smaller frequency difference in the 10s to 100s of kHz range.
For many applications, a coherence length of a mile is still
adequate. :) Of course either of the H and V components can be separated
out with a polarizer, but then the power is cut in half.

When I found the first reference, I thought it really meant pure single
mode greater than 5 mW. Nope, must read the fine print. :( :)

Reference: Robert J. Knollenberg, "Prospects for the Helium-Neon Laser Through
the End of the Century", SPIE Vol. 741, Design of Optical Systems Incorporating
Low Power Lasers (1987). The paper mentions it briefly, but has two
other references, 17 and 18 which should be more detailed. (This paper
also describes the original HP axial Zeeman laser and doesn't get it quite
right, unless it's a prototype that documented anywhere.)

There were at least two commercial transverse Zeeman stabilized HeNe laser.
The most well known (to me at least) is the Laboratory for Science 220. And,
yes, I have two working samples of this laser. ;-) The only one I know of
(at least in a product blurb) is the NEOARK NEO-262.

Scanning Fabry-Perot Interferometer Stabilization
This is a very straightforward (if challenging)
implementation in which a microcontroller essentially replaces
the human observer looking at a Scanning Fabry-Perot Interferometer (SFPI)
display of the lasing modes in real-time. See HeNe
Laser Using Scanning Fabry-Perot Interferometer for Stabilization.
This is shown for a three mode stabilized HeNe laser implementation, but
the same technique can be used with single or dual mode stabilization,
though it's not clear what, if any benefits it may provide where the simpler
alternatives described above exist. In the diagram, the tube length is such
that only three modes can oscillate when one of them is centered on the NGC.
If one is willing to accept a small amount of output on the two additional
modes that would be present with a slightly longer tube, or one that is
livelier, then a bit more power in the centered mode would be possible.
For single or dual mode polarization stabilization, the tube
would be limited to a length of around 250 mm so that two orthogonally
polarized modes would straddle the gain curve with no additional modes
present of the same polarization as the one selected for the output.

The feedback is implemented with a low finesse SFPI using the waste beam
behind the HR mirror. The low finesse results in spread out peaks, but
these are better to analyze because they can be averaged and are then less
sensitive to the exact position of the digital samples. As a result, to
reduce the space requirements for the SFPI using available mirrors,
a sub-confocal spherical or hemispherical SFPI cavity can be used
with an FSR larger than the neon gain bandwidth and a mirror spacing
of under 1 cm.

To simplify computing requirements, a dual polarization SFPI detector can
be employed. Then the orthogonally polarized modes will be separated
resulting in unambiguous determination of the polarization of the
modes of orthogoanl polarization orientation. However, for a dual
polarization detector to be effective, the
SFPI mirrors must either have zero birefringence, or their birefringent
axes must be aligned with the tube's polarization axes. Otherwise, the
mirror birefringence will overwhelm the polarization of the modes.

As with any HeNe laser, back-reflections must be minimized to the maximum
extent possible by orienting the optics such that direct reflections back
into the tube are prevented. Thus the PBS should be at a slight angle
and the SFPI should be offset and have an aperture as shown in the diagram
so that the internal reflected beams do not re-enter the laser.

A polarizing beam-splitter at the front of the laser both selects the
desired polarized mode for output and provides feedback to monitor
laser power since doing that through the SFPI may not be consistent.
Although the sampled power is of the blocked mode(s), not the output mode,
the output power can be inferred since their relative amplitudes
can be determined by the firmware. If preferred, a non-polarizing beam
sampler could be added to obtain the amplitudes of both polarized modes.
But that would reduce output power slightly.

The locking algorithm would have the same general state structure as for
the single and dual polarized mode locked except that the error terms
will be determined by analyzing SFPI data in real time to center a mode
of the desired polarization. Thus a microprocessor with higher performance
including a higher A/D sampling rate may be desirable.

Note that this is NOT quite the same as using an external reference
for locking. (More on that below.) It's still an intrinsic method
using the NGC as the reference. Thus, while drift in the SFPI due to
temperature changes or whatever is still a consideration and will
impact the locking algorithm, it will not affect he ultimate
performance in terms of absolute optical frequency accuracy or
stability.

This platform would permit any of the common techniques to be implemented
including hardware, firmware, and GUI. With its build-in SFPI, it would
also provide mode monitoring even if not used for stabilization.

Extrinsic Stabilization Techniques

These use the absorption spectrum or emission spectrum of a material -
usually a gas - as the reference. For the HeNe laser, iodine vapor
has been the preferred substance. Iodine at a controlled temperature
and pressure has numerous absorption lines in its spectrum at precisely
known locations in terms of optical frequency or wavelength. There are
about a dozen within the NGC which can act as markers for
stabilization. The most accurate commercial HeNe optical frequency
reference lasers use iodine stabilization.

The Iodine Stabilized HeNe Laser (ISHL) provides the most precise absolute
optical frequency reference in any commercial system. It is based on the
fact that iodine (or more accurately, I2 vapor) under a range of temperature
and pressure has numerous spectral absorption lines whose absolute optical
frequency is essentially fixed and known for each one. To make use of this,
the ISHL essentially locks to one of these absorption lines using
an "iodine cell" - a sealed temperature-controlled glass tube with
Brewster window termination to minimize losses and a speck of solid
iodine inside that maintains a constant pressure of I2 vapor.

However a normal internal mirror HeNe laser tube cannot be used since (1)
locking requires the use of the PDH technique involving dithering the
cavity length and (2) the dip in power due to these lines is only about
0.15 percent. At least that was the thinking of the designers of
these lasers in the 1980s. Dithering is possible. In fact, as noted,
it may occur inadvertently due to the heater characteristics. And a
special heater could be designed that maximizes rather than minimizes
this vibration. Dither could
also be introduced by a mechanical means such as a voice coil positioner
attached to one end of the tube.
This was in fact done for an axial Zeeman laser, the Spindler and Hoyer
ZL-150. so a higher power than can be provided by a single freqeuncy
HeNe laser is required. Getting enough power is perhaps more of an
issue. The solution generally used was to place the iodine cell inside
the laser cavity where a HeNe laser tube with two Brewster windows was used
as the gain medium. Putting the iodine cell inside the cavity can take
advantage of the higher circulating power there AND there would be an
amplification effect on small changes in absorption not present if
simply put in a beam with a single pass.
And PZTs on one or both mirrors would then be able
to easily dither the cavity length for the PDH locking, as well
as changing it by a larger amount to select the lock point.
But going intra-cavity creates problems of its own. Specifically
that to accomodate the length of a two-Brewster tube with enough power to
be useful AND the iodine cell, the total cavity length needs to be more
than 300 mm. It is actually around 350 mm for the Frazier version.
And as we know from previous discussions, such a long laser
will NEVER be single frequency (one mode oscillating, required
for the ISHL) unless special means are taken to force it
to be so. One method that has been used in these lasers is to introduce
sufficient losses that only a single mode has enough gain to lase. This
cam be accomplished by using a very low reflectivity output mirror - only
93% reflectance in the original NIST paper. However, deliberate misalignment
of the Brewster orientation of the laser tube and I2 cell would work just as
well and provide a means of increasing power as the tube ages. And tests of
a ISHL resonator similar to the one used by Frazier confirms an OC
reflectivity of between 0.99 and 0.994 percent. Its Radius of Curvature
(RoC) is around 60 cm which is long enough to have no impact on longitudinal
mode selection with the planar HR. The downside of any approach using such
a long cavity is than when designed or adjusted so only a single longitudinal
mode can oscillate, the available output power from the laser is order of only
100 µW! Anything higher and there will be another mode present which
cannot be removed inside the cavity. To obtain
higher power, one technique is to "offset lock" a conventional stabilized
HeNe laser to the ISHL. While strightforward, this does of course add
complexity and cost.

Some straightforward modifications would enable the cavity to be somewhat
shorter as well as simplifying maintenance. Substituting a one-Brewster
05-LHB-270 for the 05-LHB-290 would eliminate
one Brewster window and the external HR mirror, both of which can collect dust
and other contamination, as well as the additional losses from the
inner surface of the 2-B tube's second window. These tubes are otherwise
identical in size and
bore diameter. However, the internal HR mirror is not planar but probably
has an RoC of 60 cm. Apparently, putting the I2 cell close to the
planar mirror is preferred anyhow due to desire for planar wavefronts
in there. Using the 1-B tube would not permit a PZT behind
the HR, so a single PZT for the OC would be driven with the dither and line
selection PZT drive signals combined electronically. If it is necessary
to maintain the same cavity geometry, a planar mirror could be used
for the external OC.

As noted above, the use of the intra-cavity two-Brewster HeNe laser (gain)
tube and 2-B iodine cell is an established technique that works but requires
a special and expensive HeNe laser tube, requires meticulous cleanliness
of 6 optical surfaces, critical alignment, and suffers from low power.
And the low power is an inherent result of special means being required
to force single longitudinal mode operation in the necessarily long cavity.
Of course, one can't get around the need for an iodine cell, which is in
itself expensive, but perhaps there are ways to get around the other
deficiencies.

Three things must be provided for an ISHL:

Optical frequency tuning for line selection (slow and large).

Optical frequency dither for the PDH locking (fast and small).

Detection of the iodine line location.

It should be possible to implement (1) and (2) using an off-the-shelf
random polarized internal mirror HeNe laser tube suitable for a dual mode
polarization stabilizeed HeNe laser, capable of up to 2 mW or perhaps
even a bit more in a single longitudinal mode. Although a tube suitable
for three mode stabilized laser can have over 3 mW in a single mode, that
is only true when a mode is close to the center of the NGC. Go off to one
side or the other, and another mode of the same polarization will
appear, which cannot be eliminated by a polarizer or other (simple) means.
But getting around 2 mW is 20 times better than the 100 µW of the
intra-cavity ISHL.

When run at a temperature slightly above typical for lasers using
a heater surrounding the tube AND with adequate reserve power to
the heater should be able to provide an optical frequency scan rate
of one mode sweep cycle per second or better.

For dither, there are a couple of options. It may be possible using
a custom heater with the wires or conductors oriented mostly in the
longitudinal direction - parallel to the tube axis. Then, applying
an AC signal (on top of the cavity tuning signal) to the heater will
result in a fairly fast response. Since this only needs to scan order
of 1/1,000th of a full mode sweep cycle or less, it may be enough if
the heater is in intimite contact/glued to the tube.

Another possibility is to use a solenoid or voice coil positioner to
push on one of the end-caps. Any parts with magnetization must be
located away from the tube, but a small selenoid of the type used to
xmove a shutter or actuate a lock can be attached via a plastic rod
to one of the mirror mount stems and driven with an AC signal.

Getting enough sensitivity from the iodine cell may be more of a challenge.
The raw variation in absorption for the length iodine cell used in the
NIST/Frazier ISHLs is around 0.15%. With the intra-cavity implementation,
that is multiplied by circulating power of around 10 mW (100 µW output
with a 99%R OC mirror). It is also increased by being relative to the
lasing threshold by perhaps another factor of 2 or 3. So, even with a
2 mW beam, that's still a factor of 10 to 15 greater. One way to boost
the sensitivity with an external iodine cell would be to force the beam
to traverse it multiple times. With a cell of sufficient width, a pair
of planar HR mirrors could be positioned such that the beam made multiple
passes through the iodine cell. Better yet would be a custom cell that
had the mirrors inside, thus eliminating most of the losses from the
Brewster windows. Five round trips should not be difficult but
more might be possible with careful alignment. Adjacent beam should
not overlap to avoid etalon effects. Of course, such a
custom iodine cell won't be inexpensive - assuming one can find a
company willing to build such a thing. So, it may come down to
constructing one at home. More on this below. :)

Rather than requiring a possibly custom multi-pass iodine cell, a normal one
could be put inside the cavity of a high finesse SFPI. Then as the HeNe laser
tube is tuned across the NGC, the SFPI would be set up to track it while the
cavity length of the internal mirror HeNe laser tube is dithered. At an
iodine absorption line, the finesse would drop significantly due to the
additional 0.15% loss on each pass (equivalent to each mirror have a
0.15% reduction in reflectivity). The result would a dip that could
blocked using a PDH technique. Depending on the desired tuning, range,
the useful output power could be 2 to 3 mW.
Dither
Line select
External sensitivity multiplier
Multipass hall of mirrors
SFPI
Fluorescence instead of absorption detection

Where higher power or a tunable output is desired from a reference like an
iodine stabilized HeNe laser, the technique of choice is usually
"offset locking". For example, a conventional dual mode stabilized
HeNe laser can be offset locked to the ISHL by heterodying (beating)
the two lasers together and using a Phase Locked Loop (PLL) to
control the higher power laser's optical frequency. The offset can
be adjusted using a the PLL configured as a frequency synthesizer.
The offset can also be 0 Hz. In fact, this can be done with $10
in Radio Shack parts (at least when Radio Shack used to sell parts).

Even higher power is possible using a temperature-controlled intra-cavity
etalon to force single frequency in a large-frame HeNe laser, but this is
beyond what we want to deal with here. ;-)